Results 31 to 40 of about 2,144,780 (355)
Concrete quantum cryptanalysis of binary elliptic curves
IACR Cryptology ePrint Archive, 2020 This paper analyzes and optimizes quantum circuits for computing discrete logarithms on binary elliptic curves, including reversible circuits for fixed-base-point scalar multiplication and the full stack of relevant subroutines.
Gustavo Banegas +3 more
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Elliptic nets and elliptic curves [PDF]
Algebra & Number Theory, 2011 An elliptic divisibility sequence is an integer recurrence sequence associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P_1, ..., P_n are points on E defined over K.
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Generalized Fibonacci Sequences for Elliptic Curve Cryptography
Mathematics, 2023 The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves.
Zakariae Cheddour +2 more
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Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism [PDF]
Journal of High Energy Physics, 2017 We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have ...
Johannes Broedel +3 more
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A classification of isogeny‐torsion graphs of Q‐isogeny classes of elliptic curves
Transactions of the London Mathematical Society, 2021 Let E be a Q‐isogeny class of elliptic curves defined over Q. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in the Q‐isogeny class E, and an edge for each cyclic Q‐isogeny of prime degree between elliptic curves ...
Garen Chiloyan, Álvaro Lozano‐Robledo
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Elliptic curves over totally real cubic fields are modular [PDF]
, 2019 We prove that all elliptic curves defined over totally real cubic fields are modular. This builds on previous work of Freitas, Le Hung and Siksek, who proved modularity of elliptic curves over real quadratic fields, as well as recent breakthroughs due to
M. Derickx, Filip Najman, S. Siksek
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Elliptic polylogarithms and iterated integrals on elliptic curves. II. An application to the sunrise integral [PDF]
Physical Review D, 2017 We introduce a class of iterated integrals that generalize multiple polylogarithms to elliptic curves. These elliptic multiple polylogarithms are closely related to similar functions defined in pure math- ematics and string theory.
Johannes Broedel +3 more
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Elliptic Curve Cryptosystems [PDF]
Mathematics of Computation, 1987 We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially ...
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On Cycles of Pairing-Friendly Elliptic Curves [PDF]
SIAM Journal on applied algebra and geometry, 2018 A cycle of elliptic curves is a list of elliptic curves over finite fields such that the number of points on one curve is equal to the size of the field of definition of the next, in a cyclic way.
A. Chiesa, Lynn Chua, M. Weidner
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On the ρ-values of complete families of pairing-friendly elliptic curves
Journal of Mathematical Cryptology, 2012 The parameter ρ of a complete family of pairing-friendly elliptic curves represents how suitable some given elliptic curves are in pairing-based cryptographic schemes. The superiority of the curves depends on how close ρ is to 1.
Okano Keiji
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